IntegratedGradients [1]} is another approach to address gradient saturation. It does this by defining a “baseline input” \(\bar{\mathbf {x}}\) , which should represent the absence of feature information (for example, a completely gray image). The gradient of the model is then integrated along a linear path from \(\bar{\mathbf {x}}\)  to \(\mathbf {x}\) : \(E_{IG}(m, \mathbf {x}, c) = (\mathbf {x} - \bar{\mathbf {x}})\int _0^1 \frac{\partial m(\bar{\mathbf {x}} + \alpha (\mathbf {x} - \bar{\mathbf {x}}))}{\partial x} d \alpha \) . The integral is approximated using a sum of \(n\)  equidistant points along the linear path. A new problem with this approach is the choice of baseline. Depending on the circumstances, it can be difficult to choose a baseline input that is effectively “neutral”. Also, pixels that have similar values as the baseline will get under-attributed by IntegratedGradients. To mitigate this problem, ExpectedGradients [2]} uses multiple instances from the training dataset as baseline values, and averages the Integrated Gradients attributions: \(E_{EG}(m, \mathbf {x}, c) = \underset{\mathbf {x^{\prime }} \sim \mathcal {D}, \alpha \sim U(0,1)}{\mathbb {E}}\left[(\mathbf {x} - \mathbf {x^{\prime }}) \frac{\partial m(\mathbf {x^{\prime }} + \alpha (\mathbf {x} - \mathbf {x^{\prime }}))}{\partial {\mathbf {x}}}\right]\) .
